CN-116776480-B - Mechanical system analysis and experiment method based on circuit analogy

CN116776480BCN 116776480 BCN116776480 BCN 116776480BCN-116776480-B

Abstract

The invention provides a mechanical system analysis and experiment method based on circuit analogy, which provides two circuit analogy methods for a rotating mechanical system and a moving mechanical system respectively, can meet the simulation of mechanical systems with different complexity degrees, and particularly, the mechanical system is converted into an equivalent circuit by using variables in the circuit to simulate the variables in the mechanical system, the equivalent circuit is analyzed by using a circuit analysis method, and the analysis result can be directly mapped to obtain the analysis result of the mechanical system. In the aspect of analysis and calculation, the circuit calculation method is mature, the circuit steady state can be solved by a loop current method and a node voltage method, the circuit theorem is complete, the equivalent transformation principle is clear, the circuit can be simplified, the circuit time-frequency domain analysis method is mature, the small signal dynamic characteristics can be analyzed by a network function method, the circuit element has no rotating part, and the variable direction is easy to understand and represent on a plane. In the aspect of experiments, the circuit elements are rich in variety and easy to obtain, the parameters of the circuit elements are easy to measure, and the elements with the required parameters can be obtained through series-parallel connection.

Inventors

JIA FENG
WEI SHURONG
FU YANG
LI XIAOHUA

Assignees

上海电力大学

Dates

Publication Date: 20260512
Application Date: 20220310

Claims (6)

1. A method for mechanical system analysis and experimentation based on circuit analogy, comprising: step S1, according to a predetermined analog rule, analog converting the mechanical system into a corresponding equivalent circuit; step S2, simplifying the equivalent circuit by using circuit equivalent transformation and/or circuit theorem; s3, carrying out circuit analysis on the equivalent circuit to obtain a circuit analysis result; Step S4, mapping the circuit analysis result into an analysis result of a transmission system according to the analogy rule, The mechanical system is a transmission system formed by interconnecting a plurality of mechanical rotors and a plurality of flexible transmission shafts, and the basic elements of the mechanical system comprise three types: the parameter of the mechanical rotor is rotational inertia; Self-damping of a mechanical rotor, the parameters of which are friction moment coefficients, and The parameters of the flexible transmission shaft are the rigidity of the transmission shaft and the mutual damping of the transmission shaft, In step S1, the analogy rule is that the torque of the mechanical rotor is analogized by voltage, the rotating speed of the mechanical rotor is analogized by current, the self-damping of the mechanical rotor and the mutual damping of the transmission shaft are analogized by resistance, the rotational inertia is analogized by inductance, the rigidity of the transmission shaft is analogized by capacitance, the control of the torque is analogized by a controlled voltage source, the torque synthesis on the mechanical rotor is analogized by kirchhoff' S voltage law, The equation of motion of any one of the mechanical rotors is analogized to: Where J is the moment of inertia of the mechanical rotor, ω is the rotational speed of the mechanical rotor, deltaT is the resultant torque acting on the mechanical rotor, L is the inductance used to simulate the moment of inertia of the mechanical rotor, i L is the inductance used to simulate the rotational speed of the mechanical rotor, u L is the voltage across the inductance, The coefficient of friction torque generated by self-damping of any one of the mechanical rotors is analogized to: Where D is the mechanical rotor self-damping, R D is the resistance used to simulate the mechanical rotor self-damping, ω is the rotational speed of the mechanical rotor, i is the current used to simulate the rotational speed of the mechanical rotor, T D is the friction torque generated by the mechanical rotor self-damping, u D is the voltage used to simulate the friction torque, The torque analogy on any one of the flexible drive shafts is: Wherein omega 1 、ω 2 is the rotational speed of the two mechanical rotors connected with the two ends of the flexible transmission shaft respectively, K s is the transmission shaft rigidity, D s is the transmission shaft mutual damping, C is the capacitance for analogy to the transmission shaft rigidity, the value is equal to 1/K s ,R s is the resistance for analogy to the transmission shaft mutual damping, In step S3, the method includes dynamically analyzing the equivalent circuit, including the following sub-steps: s3-1, obtaining an operation circuit of the equivalent circuit by using Laplace transformation; s3-2, decomposing the operation circuit into a steady-state sub-circuit and a small-signal dynamic sub-circuit; and step S3-3, solving a network function of interest, namely a transfer function, of the small-signal dynamic sub-circuit for dynamic response analysis.
2. The circuit analogy-based mechanical system analysis and experimentation method of claim 1, wherein: wherein the mechanical system is a translation system and has thrust, speed, damping, mass and rigidity, In step S1, the analogy rule is that the thrust is analogized by voltage, the speed is analogized by current, the damping is analogized by resistance, the mass is analogized by inductance, the stiffness is analogized by capacitance, the thrust is analogized by a controlled voltage source, and the thrust synthesis is analogized by kirchhoff' S voltage law.
3. The circuit analogy-based mechanical system analysis and experimentation method of claim 1, wherein: wherein the mechanical system is a translation system and has thrust, speed, damping, mass and rigidity, In step S1, the analogy rule is that the thrust is analogized by current, the speed is analogized by voltage, the damping is analogized by conductance, the mass is analogized by capacitance, the stiffness is analogized by inductance, the control of the thrust is analogized by a controlled current source, and the thrust synthesis is analogized by kirchhoff' S current law.
4. The circuit analogy-based mechanical system analysis and experimentation method of claim 1, wherein: in step S3-3, the small-signal dynamic sub-circuit is simplified by applying the dyvenan theorem in the process of solving the network function.
5. The circuit analogy-based mechanical system analysis and experimentation method of claim 4, wherein: Wherein, step S3 further comprises: And S3-4, performing steady-state analysis on the steady-state subcircuit by adopting a loop current method or a node voltage method.
6. The circuit-analogy-based mechanical system analysis and experimentation method of claim 5, further comprising: And S5, building an actual circuit according to the equivalent circuit, the steady-state subcircuit or the small-signal dynamic circuit, and performing a simulation experiment of the mechanical system.

Description

Mechanical system analysis and experiment method based on circuit analogy Technical Field The invention belongs to the technical field of mechanical system analysis, and particularly relates to a mechanical system analysis and experiment method based on circuit analogy. Background The analysis methods of the mechanical system are conventionally adopted to build dynamic mathematical models, solve differential equations, linearize equations, analyze small signals and the like. In the analysis process, there are a plurality of problems such as difficulty in solving, difficulty in analyzing local components of the mechanical system, difficulty in deriving small signal transfer functions, and the like. Taking a transmission system in a mechanical system as an example, the direction of rotation speed and torque in the transmission system is rotatability, and in the existing analysis method, the representation is not intuitive. The experimental method also has the problem of difficult simulation, such as an equal ratio shrinkage experiment on the shaft system of the MW-level wind turbine generator, wherein the simulation of the rotary inertia disc customization, the transmission shaft rigidity and the transmission shaft damping is very difficult, the later transformation is inconvenient, the torque synthesis needs to be realized by means of complex mechanical devices such as belt pulleys, gear boxes and the like, and the two ends of the shaft system need to be provided with simulation devices capable of generating controllable torque. Disclosure of Invention The present invention is made to solve the above problems, and an object of the present invention is to provide a method for simplifying analysis and experiment of a mechanical system by a circuit analysis method based on circuit analogy, wherein the present invention adopts the following technical scheme: The invention provides a mechanical system analysis and experiment method based on circuit analogy, which is characterized by comprising the following steps: step S1, according to a predetermined analog rule, analog converting the mechanical system into a corresponding equivalent circuit; step S2, simplifying the equivalent circuit by using circuit equivalent transformation and/or circuit theorem; s3, carrying out circuit analysis on the equivalent circuit to obtain a circuit analysis result; and S4, mapping the circuit analysis result into the analysis result of the mechanical system according to the analogy rule. The mechanical system analysis and experiment method based on circuit analogy provided by the invention can also have the technical characteristics that the mechanical system is a transmission system formed by interconnecting a plurality of mechanical rotors and a plurality of flexible transmission shafts, and the basic elements of the mechanical system comprise three types: the parameter of the mechanical rotor is rotational inertia; Self-damping of a mechanical rotor, the parameters of which are friction moment coefficients, and The parameters of the flexible transmission shaft are the rigidity of the transmission shaft and the mutual damping of the transmission shaft, In step S1, the analogy rule is that the torque of the mechanical rotor is analogized by voltage, the rotating speed of the mechanical rotor is analogized by current, the self damping of the mechanical rotor and the mutual damping of the transmission shaft are analogized by resistance, the rotational inertia is analogized by inductance, the rigidity of the transmission shaft is analogized by capacitance, the control of the torque is analogized by a controlled voltage source, the torque synthesis on the mechanical rotor is analogized by kirchhoff voltage law, and the equation of motion of any mechanical rotor is analogized by: Where J is the moment of inertia of the mechanical rotor, ω is the rotational speed of the mechanical rotor, Δt is the resultant torque acting on the mechanical rotor, L is the inductance for analogy to the moment of inertia of the mechanical rotor, i L is the inductance for analogy to the rotational speed of the mechanical rotor, u L is the voltage across the inductance, and the coefficient of friction torque generated by self-damping of any one of the mechanical rotors is analogized to: Wherein D is the mechanical rotor self-damping, R D is the resistance used to simulate the mechanical rotor self-damping, ω is the rotational speed of the mechanical rotor, i is the current used to simulate the rotational speed of the mechanical rotor, T D is the friction torque generated by the mechanical rotor self-damping, u D is the voltage used to simulate the friction torque, and the torque on any one of the flexible drive shafts is simulated as: Wherein ω 1、ω2 is the rotational speed of the two mechanical rotors connected to the two ends of the flexible drive shaft, K s is the drive shaft stiffness, D s is the drive shaft mutual damping, C is the capacitance for simul